APPENDIX. The cost-effectiveness and cost-utility model.
This appendix contains the technical background and the accountability of the probabilities used in the design and construction of the Markov state-transition cost-effectiveness model.
Abbreviations and definitions used in the description
CC: cardiac complications; definition for AMC data: onset of atrial fibrillation, onset of any other rhythm disturbance needing hospitalization, pacemaker or implantable cardiac defibrillator (ICD) implantation, congestive heart failure for which hospital admittance was needed, myocardial infarction, percutaneous coronary intervention, or coronary artery bypass graft. In some literature studies the definition of cardiac complications also included angina.
Markov Correction factor: Yearly transition probability = 1-(1-tpt) 1/t in which tpt is overallprobability over time period t.
CKD stages: chronic kidney disease stages
Clinical events: ESRD, CVA or cardiac complications/event
CVA: cerebrovascular accident, as diagnosed by a neurologist
ESRD: End stage renal disease, requiring dialysis or kidney transplant (Tx)
LVH: left ventricular hypertrophy
NH: natural history
Symptoms: presence of any of the following symptoms: left ventricular hypertrophy (LVH), CKD1-4, white matter lesion(s).
WML: white matter lesion(s)
1. Aim of the Markov-analysis
The yearly costs without end-organ damage are the primary outcome measure for the cost-effectiveness analysis. The costs per quality adjusted life-year (QALY) are the primary outcome measure for the cost-utility analysis. A life-time Markov-model is constructed to include the longer term consequences of treatment.
2. Methods
Model overview
A Markov state-transition model was built, allowing the differentiation of the consecutive phases of Fabry disease. The model was programmed in Tree Age 3.5. All analyses and reports followed the existing guidelines for health technology assessment [1, 2] and decision analytic cost-effectiveness modeling [3].
2.1. Transition states
It is expected that progression to end-organ damage has the most important impact on quality of life (the utility), leading to increase of health care and non-health care costs which might be prevented by timely intervention. With the life-time Markov model the yearly costs without end-organ damage, as well as the costs per quality adjusted life year are assessed. For that purpose the model consists of 11 mutually exclusive disease states. The disease states are as follows: no symptoms (no acroparesthesia, white matter lesions, CKD1-4 or LVH present), acroparesthesia, symptoms (defined as white matter lesions, CKD1-4 or LVH present) and the complications ESRD, one or more cardiac complications (CC) or CVA and the combination of two or three complications, all as previously defined and shown in table 1. Finally, a state of death was included. In case a patient develops acroparesthesia or any of the other symptoms or disease complications, there is an indication for treatment with enzyme replacement therapy.
The model is designed to depict the prevalence and progression of disease symptoms and complications in a simulated cohort of patients with Fabry disease. The model shows a patient’s medical outcome, utility and costs per disease state, from the day of birth, until the age of 70 years or death. The length of one cycle represents 1 year.
Table 1. Transition states in the Markov model.
Disease statesNo symptoms / no LVH, CKD1-4 or wml
Acroparesthesia / acroparesthesia
Symptoms / LVH, CKD1-4 or white matter lesions
End stage renal disease (ESRD) / CKD5, dialysis or kidney transplant
Cardiac complication(s) (CC) / atrial fibrillation, any other rhythm disturbance needing hospitalization, pacemaker or implantable cardiac defibrillator (ICD) implantation, cardiac congestion for which hospital admittance was needed, myocardial infarction, percutaneous coronary intervention or coronary artery bypass graft
Cerebrovascular accident (CVA) / Stroke, as diagnosed by a neurologist
ESRD + CC / ESRD and one or more cardiac complications
ESRD+CVA / ESRD and one or more strokes
CC+CVA / One or more cardiac complications and one or more strokes
ESRD+CC+CVA / ESRD, one or more cardiac complications and one or more strokes
Dead / Death
Patients
Symptoms
The patients in the symptomatic group, including 100 patients (48 males, 52 females) with a confirmed diagnosis of Fabry disease are described elsewhere (Rombach et al manuscript included).Because of current criteria for start of ERT, patients without symptoms were not treated, with the exception of 4 patients (2 males and 2 females) who presented with acroparesthesia only. Acroparesthesia is a criterium for start of treatment but was not evaluated as predictive symptom for development of complications in the Markov model. There were few data on patients that had no symptoms at baseline and developed symptoms during follow-up (n=7, 2 males and 5 females). In addition, most patients were already known with symptoms before they were referred to the AMC outpatient clinic. Therefore age of the first presentation of acroparesthesia was estimated in the current pediatric cohort.
Complications: development of ESRD, a cardiac complication, CVA, or death.
The patients in the complication group, including 33 patients (21 males, 12 females) are described elsewhere (Rombach et al manuscript included).
2.2 Transition probabilities
The Markov state-transition model was developed with data from the Dutch Fabry registry, validated with literature data and evaluated by expert opinion. Yearly state-transition probabilities were calculated from data from the entire Dutch Fabry cohort. This cohort consisted of all registered Fabry disease patients in the Netherlands with a diagnosis of Fabry disease. Data of these patients were prospectively collected from the moment that ERT was available (from 1999). Inclusion of new patients with Fabry disease started at the beginning of the study (October 2008) up to August 2010. Prospective data were collected up to December 31st 2010. Complete follow-up data (date of birth, gender, development of clinical events and the age at the time of the clinical events) were available of 142 Fabry patients including all pediatric patients. The yearly transition probabilities for the natural (untreated) course of Fabry disease were calculated by Kaplan-Meier survival analyses, using retrospective data only.
For the analyses of the effect of ERT compared to no treatment on the transition probabilities, a distinction was made between the natural history cohort and the ERT cohort (Rombach et al manuscript included).For the analyses of the probabilities to the next disease state as visualized in the Markov decision tree, patients in the previous state were selected for calculation of the transition probability to the next state. For example, the group with symptoms was studied to calculate the rate of development of the first complication,.This implies that there is always a fixed progression of disease states from asymptomatic, through a symptomatic state and from the acroparesthesia state through a symptomatic state towards complication(s).
The yearly transition probabilities and the relative risk reduction of treatment were calculated as follows: the odds for developing a first or second complication and the contribution of age, gender and ERT duration was assessed (Rombach et al manuscript included); as in a Markov model patients enter disease states at different time points and therefore age and duration of treatment may differ, a constant yearly probability independent of age and duration of ERT was estimated. For untreated as well as treated patients, the time to the next disease state was calculated by using Kaplan-Meier analysis when 50% (or less if 50% was not reached) of the cohort in a certain state had reached the next state. Then the yearly probability was calculated by dividing the cumulative proportion (i.e. 0.50) by the median time of follow-up. These probabilities were corrected for the conditional nature of transition probabilities in the cyclic Markov model with a lifetime horizon (the Markov Correction factor:transition probability (tp)1 = 1 - (1 - tpt)1/t where tpt is the overall probabilityover time period t , see [4]. Finally the distribution of each type of complication (ESRD, CC, CVA or death) was assessed within the first, second and third complication for males and females separately when applicable and the yearly transition probability of developing a complication was multiplied with the proportion of each type of complication. For calculation of the treatment effect on the course of disease in case of initiation of ERT, the median treatment duration in each disease state of the ERT treated cohort was calculated and the odds ratio was used to calculate the relative risk reduction during that period. Then the yearly relative risk reduction was calculated, using the Markov cycle correction [4]. The yearly probability in case of ERT initiation was simply calculated as the yearly probability in the same disease stateduring the natural course multiplied by 1-relative risk reduction.
Yearly probabilities for mortality
For the mortality rate, the yearly probability of death in the different transition states was calculated as described above. The yearly probability of dying in the Fabry population was compared to the death rate of the healthy population ( survival data, as of January 24th).and in case the probability of dying in any disease state was lower in the Fabry population as compared to the healthy population (for example, patients in a disease state were young or in case of prolonging of life due to treatment effects) the background mortality was used based on the yearly survival rates (1-probability of survival).
2.3 Utilities
Yearly utility values were calculated from EQ-5D questionnaire completed by the majority of the patients in the Fabry cohort.
2.4. Costs
Yearly costs were estimated per each individual patient who also completed a questionnaire developed for this purpose. Costs consisted of indirect and direct medical costs as well as indirect non-medical costs. Volume data on inpatient and outpatient hospital care in the AMC were gathered for the full period February 2004 to November 2010 from the local hospital information system at patient level. Data on use of inpatient and outpatient health care, and sick leave were gathered quarterly by patient questionnaires between November 2008 and December 2010.All unit costs were estimated for the base year 2009. The costs, outside the AMC were calculated using the reference costs from the national health care database.
Base case analysis
In the base case analysis, the simulated cohort consists of males, females or both males (50%) and females (50%). In case a patient reaches the symptomatic state, ERT is started. Utilities for untreated and treated males and females were assumed to be similar. Similarly costs for untreated and treated males and females were the same, depending on the disease state, with the exception of the costs of ERT in case of initiation of ERT.
In daily practice, acroparesthesia can be an indication for ERT. However as there are no data published yet and the AMC data are too limited to evaluate the implication of starting relatively early in the course of disease, this scenario was not performed.
Scenario analyses
To evaluate certain treatment strategies and the impact of utilities, scenario analyses were conducted on the base case scenario. The following scenario analyses were performed for males and females:
(1) start of ERT at the age of 40 years. This is based on the fact that the mean age of start of ERT of the entire ERT cohort is 40.6 years and is comparable for males and females. It is expected that due to family screening and increased awareness the age of diagnosis will be earlier and patients will be referred to the AMC clinic at a younger age. As a consequence ERT may be initiated at a younger age and this is simulated in the base case where patients are treated as soon as symptoms are present.
(2) lower QoL during the natural course. The implications of a lower QoL in the untreated cohort was evaluated based on the literature. Data on change of health utility during the natural course and treated course are limited but it has been described that in a cohort of Fabry patients that initiated ERT the pre-treatment health utility increased from 0.64 to 0.74 [5]. The health utility scores during treatment were comparable to the AMC cohort (mean health utility 0.77). Based on these data an assumption was made that during the natural course, the utilities in each disease state were 0.1 (0.74-0.64) lower compared the utilities generated in case of ERT initiation.
(3) course of disease in patients with the classical phenotype only. Patients with an atypical phenotype have a more attenuated course of disease than patients with a classical phenotype[6]. The yearly probabilities were recalculated for the cohort without the patients with the atypical phenotype.
(4) the natural course of disease in case all patients were treated with ACE-inhibitors or angiotensin-receptor blockers. For Fabry disease there are no data published on the course of disease in patients treated with ACE-inhibitors or angiotensin-receptor blockers (ARB) as most of these have an indication and are treated with ERT. To estimate the possible impact of ACE and ARB medication, data from studies in large cohorts, at risk for renal and cardiovascular events were used to estimate the risk reduction of this type of medication[7-11]. For calculation of the risk reduction the most beneficial effect of ACE-ARB was modeled (hazard ratio of 0.70 during 2 years of follow-up) and applied to the symptomatic, and first complication group. The yearly risk reduction was calculated by correction with the Markov correction.
(5) in case patients with more advanced disease, i.e. the second complication group, would not be treated with ERT, as previous studies have doubted the beneficial effect of more severely affected patients.
(6) adding indirect costs.
Sensitivity analyses
The robustness of outcome was investigated by sensitivity analyses. This was performed through different procedures. A Monte Carlo simulation was performed to investigate the uncertainties of the yearly probabilities that were calculated. In this simulation, beta distributions were assumed for the yearly probabilities. As the AMC cohort and subgroups in this cohort were small, inherently due to the rarity of the disease, the number of patients in the actual cohort entering a new state could be less than one during one Markov cycle. In the analyzed cohort, it would be possible that no patients enter a next disease state in case the yearly probability is low. To be able to enter real integers in the Monte Carlo simulation (reflecting at least one patient experiencing an event), the lowest number of patients needed in the disease state to pass to the next state was calculated by dividing one by the yearly probability.
3. Results
Yearly probabilities
In total, data were available of 142 (58 males and 84 females) patients. At the first visit at the AMC none of them received ERT treatment.
Developing acroparesthesia and other symptoms
The age of the first presentation of acroparesthesia was estimated in current pediatric cohort (n=26). Of the 11 males, 50% had developed acroparesthesia at the age of 8 years old. The yearly probability was calculated by the proportion (0.50) divided by the median time (8 years). If corrected with the Markov factor the yearly probability of developing a first symptom was tp = 1 - (1 –0.50)1/8=0.083. Of the 15 females, 0.44 had developed acroparesthesia at the age of 12. The calculated yearly probability was 0.047.
To calculate the time to the presence of the first additional symptom (as defined previously) as accurately as possible, this was evaluated in the pediatric cohort and young adults that were referred through the pediatric outpatient clinic. This is a representative cohort, as this cohort represents both symptomatic and asymptomatic patients, mostly diagnosed through one of their adult family members. In total data of 36 patients fulfilled the criteria, of which 3 pediatric males and 3 pediatric females had no complete evaluation yet and were not included in the analysis. Of this cohort (12 males and 18 females), the median time the first symptoms was 17.4 years. The yearly probability was calculated by the proportion (0.50) divided by the median time to the first symptom (17.4 years). If corrected with the Markov factor the yearly probability of developing a first symptom was 0.039.
The rate of developing another symptom (as defined previously) was the same for the pediatric patients with and without acroparesthesia (probably due to the small size of the cohort). Therefore the 50% of the males and females with acroparesthesia would develop a symptom within 9.4 (17.4-8) and 5.4 (17.4-12) years respectively. Therefore the rate of developing a symptom in case of acroparesthesia in females was higher compared to males.
Symptoms, developing the first complication: ESRD, a cardiac complication, CVA or death.
At the time of the first evaluation at the AMC, 48 females presented with symptoms compared to 46 males. At that time 7 females had developed the first complication and the median time to the first complication was 66.0 years. Of the 46 males, 12 males had experienced a first complication after a median age of 53.3 years. The time patients developed their first symptom could not be ascertained for most (adult) patients. Some patients were diagnosed relatively late in the course of disease while probably already having undiagnosed symptoms for years. Therefore the median time to the first presentation of symptoms in the pediatric cohort was used. Therefore the median time between the first presenting symptoms and the first complication for males was (53.3-17.4) 35.9 years. The yearly probability was calculated as the proportion of patients that developed a cardiac complication, ESRD, stroke, or death, divided by 35.9 years, corrected with the Markov correction. In females, the time to the first complication was 66.0 years. Similarly to males, the median time to the first presenting complication was calculated as (66.0-17.4) 48.6 years.